The oxygen absorbance was studied at wavelengths 200–270 nm in Schumann-Runge system behind the front of a strong shock wave. Using these data, the vibrational temperature Tv behind the front of shock waves was measured at temperatures 4000–10 800 K in undiluted oxygen. Determination of Tv was based on the measurements of time histories of absorbance for two wavelengths behind the shock front and on the results of detail calculations of oxygen absorption spectrum. Solving the system of standard quasi-one-dimensional gas dynamics equations and using the measured vibrational temperature, the time evolution of oxygen concentration and other gas parameters in each experiment were calculated. Based on these data, the oxygen dissociation rate constants were obtained for thermal equilibrium and thermal non-equilibrium conditions. Furthermore, the oxygen vibrational relaxation time was also determined at high temperatures. Using the experimental data, various theoretical and empirical models of high-temperature dissociation were tested, including the empirical model proposed in the present work.

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The evolution of oxygen molecule vibrational temperature behind the front of a shock wave was studied at shock wave velocities 3 4.5 km/s and gas pressure ahead of the shock front 1 5 Torr. The results of vibrational temperature measurement con¦rmed the conception of separation of vibrational relaxation and dissociation zones behind the shock wave front at T ≤ 6500 K. It is observed that at T = 6500 10 500 K the vibrational temperature decreased in comparison with its value characterized by the achievement of vibrational translational equilibrium before the dissociation started. It is shown that the model should to be modi¦ed to describe the evolution of the oxygen vibrational temperature under the conditions of vibrational relaxation and dissociation coupling.

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In this paper are developed modifications of the Godunov scheme, based on Kolgan's scheme of the second order of accuracy in the spatial variables for smooth solutions. It is constructed schemes of the first and the variable order of approximation, which exceed the Godunov scheme in accuracy. Referencing to the system of differential equations for propagation of flat sound waves in a gas at rest, the Kolgan scheme and the first-order schemes obtained are investigated onto the ability to ensure the non decrease of entropy, that is, to product of physically justified numerical solutions.The test problems of nonlinear gas dynamics on the decay of a discontinuity in a pipe and the transformation of a non uniformity in a plane-parallel flow are solved. Cylindrical explosion task is considered as the main one. The stability of a contact discontinuity behind a blast wave is investigated numerically in the Cartesian and polar coordinate systems. Analysis of obtained and published solutions does not confirm the instability of the contact discontinuity which initially has the circular shape. Change of the shape of initially perturbed break is largely caused by the instability of Taylor, not Richtmyer-Meshkov. Calculations are partially fulfilled using supercomputer "Lomonosov" of Moscow state university.

The feasibility of steady detonation combustion of a hydrogen-air mixture entering at a supersonic velocity in an axisymmetric convergent-divergent nozzle with a central coaxial cylinder is considered. The problem of the nozzle starting and the initiation of detonation combustion is numerically solved with account for the interaction of the outflowing gas with the external supersonic flow. The modeling is based on the gasdynamic Euler equations for an axisymmetric flow. The calculations are carried out using the Godunov scheme on a fine fixed grid which allows one to study in detail the interaction of an oblique shock wave formed in the diffuser with the nozzle axis. It is shown that a central coaxial cylinder ensures the starting with the formation of supersonic flow throughout the entire nozzle and stable detonation combustion of a stoichiometric hydrogen-air mixture in the divergent section of the nozzle.

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